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Symmetric Bernoulli distributions and minimal dependence copulas

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  • Alessandro Mutti
  • Patrizia Semeraro

Abstract

The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli variables, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas corresponding to symmetric Bernoulli vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties.

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  • Alessandro Mutti & Patrizia Semeraro, 2023. "Symmetric Bernoulli distributions and minimal dependence copulas," Papers 2309.17346, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2309.17346
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    References listed on IDEAS

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    1. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
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